How do solve $x^3+2x^2<=8x$ and write the answer as a inequality and interval notation?

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How do solve $x^3+2x^2<=8x$ and write the answer as a inequality and interval notation?

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Answer 1 · 2016-10-24T13:15:00

The answer is $-oo<=x<=-4$ and $0<=x<=2$

Explanation:

Let us factorise the inequality and make a sign chart

$x^3+2x^2-8x<=0$

$x(x^2+2x-8)<=0$

$x(x-2)(x+4)<=0$

So the values are $x=0$ , $x=2$ and $x=-4$

$x$ $color(white)(aaaaa)$ $-oo$ $color(white)(aaaaa)$ $-4$ $color(white)(aaaaa)$ $0$ $color(white)(aaaaa)$ $2$ $color(white)(aaaaa)$ $+oo$
$x$ $color(white)(aaaaa)$ $color(white)(aaaa)$ $-$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$
$x-2$ $color(white)(aaaa)$ $color(white)(aa)$ $-$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$
$x+4$ $color(white)(aaaa)$ $color(white)(aa)$ $-$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$
$X$ $color(white)(aaaaaa)$ $color(white)(aa)$ $-$ $color(white)(aaaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$
So the answer is $-oo<=x<=-4$ and $0<=x<=2$

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How do solve $x^3+2x^2<=8x$ and write the answer as a inequality and interval notation?

1 Answer

Explanation:

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How do solve $x^3+2x^2<=8x$ and write the answer as a inequality and interval notation?